Investigation into how the concentration of a metal ion affects the hardness of water.

Investigation into how the concentration of a metal ion affects the hardness of water

Introduction

Water that forms a lather with soap is called soft water. Hard water is water that does not form a lather with soap, due to impurities in the water. Hard water is safe to drink, colourless, odourless and tastes exactly the same as soft water. However, it contains chemical impurities e.g. substances other than water. The impurities that cause hardness in water are usually calcium and/or magnesium ions.

Tap water is normally obtained from springs and rivers, and the hardness of the water varies according to the types of rocks and soil through which the water has flowed on its way to the reservoir. Gypsum (calcium sulphate) is slightly soluble in water, and as the water flows past, a small amount of calcium sulphate dissolves in the water, causing hardness. Limestone (mainly calcium carbonate) is another rock that can result in the formation of hard water, although the rock itself does not dissolve in pure water. Instead, the calcium carbonate is dissolved by the natural carbonic acid in rainwater. When rain falls from the clouds, it dissolves some of the carbon dioxide in the air, forming carbonic acid:

H2O(l) + CO2(g) H2CO3(aq)

When the carbonic acid comes into contact with limestone, it dissolves the calcium carbonate, forming calcium hydrogencarbonate in a solution:

CaCO2(s) + H2CO3(aq) Ca(HCO3)2(aq)

This is why hard water is very common in areas with major limestone deposits (see diagrams on the left).

There are two types of hardness:

Temporary hardness
Permanent hardness

Temporary hardness is cause by the hydrogencarbonates of calcium and magnesium, and can be reduced or removed by boiling the water. Calcium hydrogencarbonate is decomposed when heated; producing carbon dioxide and water and forming a calcium carbonate precipitate which is called limescale. The calcium ions are no longer available to react with the soap and produce a scum.

Ca(HCO3)2(aq) CaCO3(s) + CO2(g) + H2O(l)

Hardness that is not removed by boiling the water is called permanent hardness. Calcium and magnesium sulphates and chlorides cause permanent hardness.

Soap is a type of detergent (cleaning agent). Sodium stearate is a type of common soap. The atoms are arranged in a long chain, with a head and a tail. The tail is made up of a long chain of carbon atoms, and there are seventeen of them in this example. Hydrogen atoms are attached to the carbon atoms. The head is made up of a group of atoms, two oxygen, one carbon and one sodium atom, which is joined ionically to the other atoms. When sodium stearate enters water, the sodium ions separate from the rest of the atoms. The atoms of oxygen become negatively charged. This end of the group of atoms is attracted to the water molecules. The other end is attracted to grease and dirt but is repelled by the water. The result is that when something is washed in soapy water, the particles of grease and dirt are dislodged, but the charged particles are kept separate and the grease or oil becomes emulsified.

When soap interacts with hard water, the stearate ions combine with the calcium and magnesium ions to form insoluble calcium and magnesium compounds. These compounds are called scum. The soap ions are no longer free in the water, so there is no lather and the soap has little effect. Soap can only produce a lather in hard water when all of the calcium ions have reacted with the stearate ions. Then, the excess stearate ions can emulsify the grease or oil.

Apparatus

50cm3 burette × 1 Stopwatch × 1

25cm3 measuring cylinder × 1 Goggles × 1

50cm3 measuring cylinder × 1

10cm3 measuring cylinder × 1

100cm3 conical flask + rubber bung × 1

Thermometer × 1

Teat pipette × 1

Distilled water + bottle × 1

Funnel × 1

Variables table

Preliminary work

Preliminary work was conducted to find out which metal ions cause hardness in water, so that a suitable ion that causes hard water can be used in the experiment to react with the soap solution.

The apparatus used in the preliminary work consisted of:

Test-tube

Test-tube rack

Cork

10cm3 measuring cylinder

Distilled water

Goggles

The independent variable in the preliminary experiment was the different test solutions containing different metal ions. The dependent variable was the appearance of a lather. The surrounding temperature, way and length of time of shaking, the volume of soap solution and ...

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Preliminary work

Preliminary work was conducted to find out which metal ions cause hardness in water, so that a suitable ion that causes hard water can be used in the experiment to react with the soap solution.

The apparatus used in the preliminary work consisted of:

Test-tube

Test-tube rack

Cork

10cm3 measuring cylinder

Distilled water

Goggles

4cm3 of sodium chloride solution was put in a test-tube. Ten drops of soap solution were then added. The test-tube was shaken for 10 seconds for as hard as possible. Then the test-tube was observed for the presence of a lather.

The test-tube was then washed out thoroughly with distilled water, since the distilled water would not react with the metal ions. This was then repeated twice, and the experiment was also done for calcium chloride, magnesium chloride, potassium chloride, magnesium nitrate, calcium nitrate, magnesium sulphate and sodium sulphate.

Results from preliminary work

Conclusion from preliminary work

From the preliminary results, it can be concluded that it is the metal ions (cations) that cause hardness in water, not the anions. This is because for the solutions containing chloride, the sodium chloride solution produces a lather in water after shaking, but calcium chloride and magnesium chloride form a scum, not a lather. The same applies for the nitrate solutions, where potassium nitrate forms a lather in water but magnesium nitrate and calcium nitrate do not. Sodium sulphate produces a lather in water, but magnesium sulphate does not.

Since it can be concluded that anions do not cause hardness in water, then it must be the metal ions that cause hard water. While the solutions containing potassium and sodium ions all formed lathers, none of the solutions containing calcium or magnesium formed lathers. All of the calcium ion solutions and magnesium ion solutions formed scum in water after shaking. Therefore, it can be concluded that calcium and magnesium ions cause hardness in water. In the main experiment, I will use and vary the concentrations of calcium ion solution to react with the soap solution.

Experiment Method

This method will use the apparatus mentioned in the list.

Goggles will be put on before the experiment and worn for the duration of the experiment to protect the eyes from being irritated by the soap solution or calcium ion solution.

The burette will be clamped to a stand, and the tap will be closed. The burette will be filled with soap solution containing stearate ions, using a funnel to ensure that the soap solution is not spilt. If necessary, the burette and stand can be placed on the floor to ensure that the funnel is not above eye height, reducing the chance of knocking over the burette while filling it up. The burette has been chosen to contain the soap solution because it is the most accurate piece of equipment available, accurate up to 0.05cm3. The funnel will be taken out, and some soap solution should be let out of burette into a test tube. This fills up the capillary below the tap of the burette, ensuring that the volume of the soap solution in the burette always includes the soap solution in the capillary for each concentration of calcium ions. This is a control variable. The starting volume of soap solution in the burette will be recorded to the nearest 0.05cm3, taking the reading at the bottom of the meniscus at eye level. A white tile should be placed behind burette so that the level of soap solution is clear.

An ion that causes hard water will be used to react with the stearate ions and form a scum, before a lather is formed. From preliminary work, it has been shown that all calcium and magnesium ions cause water to be hard. In this experiment, calcium ions will be used to react with the soap solution. The calcium ion solution will be diluted to different concentrations. However, the overall volume of the solution will always be the same, and this is a control variable and cannot be changed. The overall volume of the solution will be 40cm3, and this is a suitable volume because it is large enough to get an accurate result without using excessive amounts of both calcium ion solution and soap. Distilled water will be added to varying amounts of calcium ions to maintain the overall volume of 40cm3. Distilled water will be used because it does not contain any impurities that may affect the reaction of calcium ions and soap ions, whereas tap water may be hard itself, and react with the soap solution. The table below shows the different concentrations of calcium ions, and the volumes of calcium ion solution and distilled water needed to form the different concentrations.

A total of eight concentrations will be used, as this will provide a suitable amount of evidence for the analysis. For each concentration, the experiment will be repeated three times and an average will be taken from the three results. This will increase the accuracy of the results by reducing the effects of anomalies.

To achieve a concentration of 12.5% calcium ions, 5cm3 of calcium ion solution will be poured into a 10cm3 measuring cylinder from the main flask, using a funnel. A teat pipette will be used to ensure that the bottom of the meniscus falls exactly on 5cm3 at eye level. This increases the accuracy of the measurement. The 5cm3 of calcium ion solution will then be poured into a conical flask. The 10cm3 measuring cylinder will be washed out thoroughly with distilled water to ensure it is not contaminated with calcium ions. This is because distilled water does not contain any impurities, and using it to wash out apparatus will not have any effect on the results.

35cm3 of distilled water should be poured into a 100cm3 measuring cylinder. A teat pipette should be used to make sure that the bottom of the meniscus is level with the 35cm3 mark on the measuring cylinder at eye level. The distilled water will also be poured in the conical flask, making the total volume in the conical flask 40cm3. The concentration of the calcium ions in the conical flask will be 12.5%. The 100cm3 measuring cylinder will be washed out with distilled water.

The conical flask will be placed on a white tile under the burette. The tap will be opened, and the soap solution will fall into the conical flask from the burette. Every 5cm3 of soap solution, the tap should be closed. A bung will be used to seal the mixture of soap solution, calcium ions and distilled water, and the conical flask should be shaken for ten seconds for as hard as possible. This is a control variable. If there is no lather formed, then the bung will be removed and more soap solution will be added. As soon as any lather is formed, the soap solution should be added dropwise (0.05cm3). The end point is when the lather formed lasts for ten seconds before disappearing. This is a control variable and applies for all concentrations. The end volume of soap solution in the burette will be measured from the bottom of the meniscus at eye level, and will be taken away from the starting volume of soap solution to show how much soap solution has been used to form a lather lasting ten seconds. This is the reading that is recorded.

The experiment for this concentration will be repeated twice so that there are three readings, and an average will be taken. The experiment will then be repeated for the other concentrations of calcium ions in the table.

Prediction

My main prediction is that as the concentration of calcium ions increases, the volume of soap required to produce a lather lasting ten seconds will also increase. My second prediction is that as the concentration of calcium ions doubles, the volume of soap required to produce a lather lasting ten seconds will also double.

As the concentration of calcium ions increases, the number of calcium ions in the calcium ion solution will also increase. As a result, there are more calcium ions available to react with the stearate ions. More stearate ions are needed to form compounds with the extra calcium ions. Additional stearate ions are needed to form a lather after all the calcium ions have reacted. Therefore, more soap solution is required to form a lather when there is higher concentration of calcium ions. This is the theory that my prediction is based upon.

The ionic symbol equation that shows the reaction between calcium ions and stearate ions to form a compound is:

Ca2+(aq) + 2St-(aq) CaSt2(s)

From this, it is shown for every calcium ion, two stearate ions are required to form a compound. The calcium ion has two positive charges but the stearate ion only has one negative charge, so two stearate ions (one negative charge each equalling two negative charges altogether) are required to balance the calcium ion (two positive charges). This makes the resulting compound neutral. The number of stearate ions should always be double the number of calcium ions for this to be a balanced equation.

If the number of calcium ions double, the number of stearate ions should also double. This is because with two calcium ions, there are four positive charges, so there needs to be four stearate ions with one negative charge each to form the neutral compound. The table below shows how increasing the number of calcium ions affects the number of stearate ions and the quantity of the resulting compound.

The graph will have the concentration of calcium ions on the x-axis and the volume of soap solution used to make a lather on the y-axis. I predict that the graph will be a straight line graph, and could be explained using the equation for straight lines, y=mx+c. The straight line will not pass through the origin, as some soap is needed to produce a lather at 0% concentration of calcium ions (pure water). This is because the lather is produced by the stearate ions and if there is no soap, there will not be any stearate ions, meaning no lather even in pure water. The graph should resemble this:

Results table

Graph

Analysis

The evidence shows that as the concentration of calcium ions in water increases, the volume of soap needed for a lather to be produced increases, so the results support the basic prediction. The graph clearly shows a linear relationship between concentration of calcium ions and volume of soap, with a straight line of best fit that does not pass through the origin ( (0,0) ). 6 out of 8 points lie on the line so the results are very accurate. The graph shows one anomaly in the results.

The volume of soap added to form a lather increases when the concentration of calcium ions increases, because the soap can only form a lather once all of the calcium ions have reacted. The calcium ions and soap ions form an insoluble precipitate called scum and this prevents a lather from forming. To form a lather, all the calcium must already have reacted with soap ions. Then the remaining soap ions cause a lather to form in the water. When the number of calcium ions increases, the number of soap ions needed to react with all of the calcium ions must also increase for a lather to form.

The anomaly in the results is at 62.5% concentration of calcium ions and is not anywhere near the line of best fit, so it almost certainly erroneous. This may have been due to the control variables not being controlled sufficiently tightly, or due to the end point not being defined accurately enough.

The line of best fit does not pass through the origin because some soap is needed for any lather to be formed. Without soap, there are no stearate ions, therefore no lather can be formed at all, and the 3cm3 of soap needed to form a lather without any calcium ions present is necessary for even pure water. This is why the line of best fit does not pass through the origin.

The graph can be represented using the equation y=mx+c, since it is a straight line graph. “y” represents volume of soap on the y-axis, while “x” represents the concentration of calcium ions on the x-axis. “m” is the gradient of the line, and “c” is the intercept point. The gradient can be worked by dividing the y-value minus the intercept (c) of a point on the line by the x-value. The table below shows how the gradient was worked out:

The expression that describes the line on the graph is y=0.32x+3. This confirms the prediction, which states that the graph can be described by this type of equation. The table below shows how this line confirms the precise accuracy of the results.

The table shows that the y value worked out using the equation y=0.32x+3 is very close to the actual y value taken from the results. This shows that the results are accurate and have very strong correlation, because almost all the points fit on the best fit line, which is the line described by the equation.

The volume of soap at the intercept point (3cm3) can be taken away from the other volumes. Then, only the soap used up by the calcium ions to form a lather comes in account. When this is done, it shows that as the concentration of calcium ions doubles, the volume of soap needed to produce a lather also doubles. The table at the top below shows examples of this.

From the table, it is evident that when the concentration doubles from 10% to 20%, the volume of soap does not double. However, once the intercept volume is taken away, it can be shown that the volume of soap does indeed double. Using the figures highlighted in red, it is clear that when the concentration of calcium ions doubles from 10% to 20%, the volume of soap required to form lather also doubles, since:

6.25 / 3.1 = 2.02 (2DP). 6.25 is very close to double 3.1, so it can be concluded that doubling the concentration of calcium ions also doubles the volume of soap required to form a lather. The results in blue also show this, since:

Concentrations of calcium ions: 80 / 40 = 2

Corresponding volumes of soap: 25.5/12.75 = 2

The results can also be explained using the symbol equation:

Ca2+(aq) + 2St-(aq) CaSt2(s)

The table on the left shows how increasing the number of calcium ions affects the number of stearate ions and the quantity of the resulting compound. From this, it is shown for every calcium ion, two stearate ions are required to form a compound. The calcium ion has two positive charges but the stearate ion only has one negative charge, so two stearate ions (one negative charge each equalling two negative charges altogether) are required to balance the calcium ion (two positive charges). This makes the resulting compound neutral. The number of stearate ions should always be double the number of calcium ions for this to be a balanced equation.